Labor market impacts of destructive California wildfires

For estimating how an outcome would differ since an event occurred as compared with if no event had occurred, a generalized difference-in-difference (GDD) modeling approach is used with an event-study specification. The GDD approach estimates the impact of exogenous shocks, such as wildfires, on employment over time, by comparing employment in counties and periods with wildfires with employment in counties without wildfires. However, unlike a standard GDD approach in which a single difference (such as first differences or 12-month difference) is used and only measures the impact of an event in the month of the event, separate +h-difference models are estimated in an event-study setup in which h goes from 0 through 18 months. This method allows estimation of the temporal impacts of wildfire events. That is, the impacts of wildfires on employment are estimated for each month after the event for 18 months, as compared with the period before the fire (t – 1). The degenerate case of h=0 is a standard first difference in a GDD model and measures the impact of an event in the month of the event.

As with standard panel data analysis, the analysis first pools (or stacks) the cross-sectional data (counties) across time (months or quarters) and denotes the labor market outcomes, Y (relative employment percent change), in county, c, at time, t, by Yct. Since growth rates of the outcomes between two periods—the month before an event (t – 1) and h-months after an event (t + h)—are examined, the natural log of Yct is used and rewritten as h+1-differences: ln Yc,t+h − ln Yc,t−1, where h goes from 0 to 18. Similarly, this h+1-month difference for California statewide is computed and then removed from each county as a general state-level business cycle detrending. This detrended percent change is defined as.

The empirical model is expressed as

where L, M, and S are indicators for large, medium, and small fire events. The main coefficients of interest are,, and and represent the beyond expected percent change (as compared with periods of no fires) in a labor market outcome relative to the period before an event, h months after a fire event. For example, changes in employment 1 year after a fire event for counties that had large fires are compared with employment changes of all 1-year periods in all counties where no fire event occurred. Also, γk captures the coefficients on k-period-lagged first differences, a way to capture and control for the effects of economic momentum. The analysis in this article estimates this model for all integer values of h from 0 through 18, that is, for each month up to 18 months since a potential fire event. The variation in the error term comes from randomness in timing and counties. In the model just described, the counties and periods after a fire event are the “treatment” group and the counties and/or periods without a fire event are the “control” group.

After the transformation of these data, the model is estimated by using ordinary least squares procedures for each outcome and h. For conciseness and more general results, these estimates are averaged into quarterly categories. For example, “Q1” (quarter 1) indicates the average of months 1 through 3 following the month of a fire event, Q2 (quarter 2) indicates the average of months 4 through 6 following the month of a fire event, and so forth.

For each of the summarized estimates of the time categories, standard errors are computed via bootstrap resampling. For each recomputation, the fire-size indicators are sampled with replacement (randomly assigning) across counties and time. Bootstrap standard errors and 95-percent confidence intervals are formed from 10,000 replications. The idea is to form bootstrapped distributions of potential estimates such that the null hypothesis is that wildfires have no impact on the outcomes. The resulting bootstrapped distribution of estimates represents the potential values an estimate may take when no underlying impact exists from fires (randomly assigned across counties and time). Estimates from the model that fall in the lower or upper 2.5 percentile of the distribution indicate statistical significance at the 5-percent alpha level.